The act is condemned by Turkey as a “serious threat” to regional peace.
In a letter to the UN Security Council, Turkey described the incident as a “hostile act by the Syrian authorities against Turkey’s national security”.
Turkey’s deputy prime minister said it “would not go unpunished”, but stressed it was not seeking military action.
Damascus insists the F-4 Phantom jet was shot down inside Syrian airspace.
In the letter to the Security Council, Ankara said the shooting down of its F-4 reconnaissance plane was “a serious threat to peace and security in the region”.
The letter does not ask the council to take any action.
Turkish PM Recep Tayyip Erdogan is expected to outline his next step when he addresses parliament on Tuesday.
Turkey, a NATO member, has requested a meeting of the alliance’s ambassadors in Brussels after invoking Article 4 of NATO’s founding treaty, which entitles any member state to request consultations if it believes its security is threatened.
This is believed to be only the second time in NATO’s history that a member state has invoked Article 4. In 2003, Turkey asked for NATO assistance to ensure its security in the run-up to the Iraq war.
A NATO official quoted by AP news agency said Turkey’s NATO envoy would inform other ambassadors of the details of the incident at Tuesday’s meeting.
The envoys are then expected to discuss Turkey’s concerns but not decide on anything specific, said the official.
The North Atlantic Council – which consists of ambassadors from all 28 NATO countries – works by consensus and all members must approve any action.
Deputy Prime Minister Bulent Arinc, speaking after an emergency cabinet meeting on Monday, called the shooting down of the jet “a hostile act of the highest order”.
He vowed that Syria would “not go unpunished” but added that Turkey had “no intention” of going to war.
“We don’t believe warmongering or provoking the crowds by being righteous is the right thing to do. What needs to be done will be done within a legal framework,” he said.
Tensions between Syria and Turkey rose even higher on Monday when Turkey accused its neighbor of firing on another of its planes.
Bulent Arinc said the CASA search and rescue plane – which had been looking for the F-4 Phantom jet – was not brought down.
He said the Syrians stopped firing after a warning from the Turkish side.
Ankara has said the jet strayed into Syrian airspace by mistake last Friday but was quickly warned to change course by Turkish authorities and was one mile (1.6 km) inside international airspace when it was shot down.
Syria said it was unaware that the plane belonged to Turkey and had been protecting its air space against an unknown intruder.
But in its letter to the UN Security Council, Turkey says that intercepted radio communication shows that Syrian units were fully aware of the circumstances of the flight.
Relations between the two countries were already highly strained before the F-4 was shot down.
Recep Tayyip Erdogan has been outspoken in his condemnation of Syrian President Bashar al-Assad, whose government he accuses of brutally putting down opposition protests.
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